Kinematics of Machinery Unit 1

7/24/2019 Kinematics of Machinery Unit 1

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KINEMATICS OF MACHINERY

MEE 215

KHALID/SMBS/VITU/WINTER 201516 15/01/2016


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Can crusherSimple press

Examplefor Mechanism

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Rearwindow

wiper Lift platform



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Moves packages from an assembly

bench to a conveyor

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TERTIARY LINK

BINARY LINK

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Microwave carrier to assist

people on wheelchair

Lift platform


CAN SLIDE

AND ROTATE

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Front loader

Device to

close the top

flap of boxes



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Rowing type exercise machine Conceptual design for an

exercise machine



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Machines

Machine: an assemblage of parts

(components) that transmit forces, motion

and energy in a predetermined manner.

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Machines

A machine is a combination of rigid orresistant bodies, formed and connected so

that they move with definite relative motions

and transmit forces from the source of powerto the resistance to be overcome.



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Machines

A machine has two functions:

1. transmitting definite relative motions, and2. transmitting forces.

These functions require strength and rigidity

to transmit the forces.



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Mechanisms

A mechanism defined as a

combination of rigid or resistant

bodies, formed and connected so

that they move with definite

relative motions with respect to

one another.



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Machines Vs Mechanisms

The similaritybetween machinesandmechanismsisthat:

They are both combinations of rigid bodies

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Structures

Astructureis an assembly of rigid or resistant bodieswith nonmovable joint for load bearing purpose.

Structure does not have internal mobility (No relative

motion)

Machines and Mechanisms have internal mobility

Usually static deals with structures

Kinematics and Kinetics deal with the Mechanics and

Mechanisms

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Some Important Definitions



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Links or Elements

A link is defined as a rigid body having two or

more pairing elements which connect it to otherbodies for the purpose of transmitting force or

motion OR

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Links (completely rigid)

Crank Pin

Crank Shaft Flywheel

Identify which

link is fixed?



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Links (Not rigid)

Springs

Belts

Ropes



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Links

Links are connected to transmit motion From Driver (input link)

To Driven or follower (output link)

Links Unitary ( singular),

Binary,

Ternary or

Quaternary.



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Links



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Kinematic Pairs

Two elements or links are connected togetherin such away that their relative motion is

completely constrained form a kinematic

pair. or

A joint of two links having relative

motion between them.



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Kinematic Pairs Types

Types

Higher Pairs (point, Line or Curve contact)Gear teeth, cam and follower, friction disks

Lower pairs (Surface Contact)

1. Revolute joint (Pin joint) such as hinges

2. Prismatic pair such as sliders



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Six Types of Lower Pairs



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Higher pair:

The contact between the pairing elements takes place at a point or along a line.



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Kinematic Chain

When several movable links are connected to eachother by joints, they are calledkinematic chain.

A kinematic chainwith at least one link has beengrounded constitutes a mechanism chain.



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Closed Chain

Ifevery link in the chain is connected to two or morelinksthen the chain form one or more closed loops

If the link form a closed loops, it is called closedmechanism chain

IfNOT, the chain is said to be open mechanism chain



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Planar and Spatial Mechanisms

In planar mechanisms, all of the relative

motions of the rigid bodies are in one plane or

in parallel planes

If there is any relative motion that is not in the

same plane or in parallel planes, the

mechanism is calledspatial mechanism.



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Degrees of freedom (DOF)

The definition of theDegrees of Freedomof a

mechanism is the number of independentrelative motions among the rigid bodies.



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Mobility

The number of degrees of freedom of a mechanism

is also called themobilityof the device.

DOFswithnumberjo

DOFswithnumberjo

JJnhjnM

2intJ

1intJfreedom)ofdegrees(twopairshigherofnumberh

freedom)ofdegree(onepairslowerorjointsbinaryofnumberj

frame)the(includinglinksofnumbern

mechanismin thefreedomofdegreestotalM

Where

.12)1(32)1(3

2

1

21

TheKutzbach criterion



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Degrees of freedom/mobility of amechanism

It is the number of inputs (number of independent coordinates) required to describe

the configuration or position of all the links ofthe mechanism, with respect to the fixed linkat any given instant.



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Examples DOF

F = 3(n-1)-2J-h

Here, n = 4, J = 4 &

h = 0.

F = 3(4-1)-2(4) = 1 I.e., one input to any one

link will result in definite

motion of all the links.



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F = 3(n-1)-2J-h

Here, n = 5, l = 5 and h = 0. F = 3(5-1)-2(5) = 2

I.e., two inputs to any two links arerequired to yield definite motions inall the links.

F = 3(n-1)-2J-h

Here, n = 6, l = 7 and h = 0.

F = 3(6-1)-2(7) = 1

I.e., one input to any one link will result indefinite motion of all the links.



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DOF ?

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F = 3(n-1)-2J-h Here, n = 6, l = 7 (at the intersection of

2, 3 and 4, two lower pairs are to beconsidered) and h = 0.

F = 3(6-1)-2(7) = 1

F = 3(n-1)-2J-h

Here, n = 11, l = 15 (two lowerpairs at the intersection of 3, 4,

6; 2, 4, 5; 5, 7, 8; 8, 10, 11) andh = 0.

F = 3(11-1)-2(15) = 0



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Calculate the degrees of freedom of the mechanisms

shown in Figure.

Here , n = 4, l = 4 ( at A, B,C,D) and h = 0.

F=3(4-1) -2 x 4-0 = 1

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LOCKED CHAIN OR STRUCTURE

Links connected in such a way that no relativemotion is possible.



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Unconstrained kinematic chain



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MECHANISM

Slider crank and four bar mechanisms


Find DOF ?


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(a)

F = 3(n-1)-2l-h

Here, n = 4, l = 5 and h = 0.

F = 3(4-1)-2(5) = -1

I.e., it is a structure

(b)

F = 3(n-1)-2l-h

Here, n = 3, l = 2 and h = 1.

F = 3(3-1)-2(2)-1 = 1

(c)

F = 3(n-1)-2l-h

Here, n = 3, l = 2 and h = 1.

F = 3(3-1)-2(2)-1 = 1



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F = 3(n-1)-2l-h

Here, n = 9, l =11 and h = 0.F = 3(9-1)-2(11) = 2

F = 3(n-1)-2l-hHere, n = 8

l = 9+2(on account of double joint),h = 0.

F = 3(8-1)-2(11) = -1

F = 3(n-1)-2l-h

Here, n = 10,l = 9+2(2)=13 and

h = 0.

F = 3(10-1)-2(13) = +15/01/2016


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F = 3(n-1)-2l-hHere, n = 9,

l = 11 and

h = 0.

F = 3(9-1)-2(11) = +2

F = 3(n-1)-2l-hHere, n = 7,

l = 8 and

h = 1

F = 3(7-1)-2(8)-1 = +1

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F = 3(n-1)-2l-hHere, n = 9,

l =11 (one DOF)

h = 1F = 3(9-1)-2(11)-1 = +1

Fig. Undercarriage mechanism of an aircraft

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Kinematic Equivalence


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Kinematic Equivalence

Higher pair joints are often replaced by kinematically equivalent lowerpair joints.


3

2

11

2

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n=2

l=1

h=0

F=1

n=3

l=2

h=0

F=2

n=4

l=4

h=0F=1

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n=4l=3

h=0

F=3

n=6

l=7h=0

F=1

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Find DOF ?


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F = 3(n-1)-2l-hF=3(10-1)-2(12)=+3

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Find DOF ?


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F = 3(n-1)-2l-h= 3(10-1)-2(12)=+3

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Grublers criterion for plane Mechanisms


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Grubler s criterion for plane Mechanisms

The Grublers criterion applies to mechanisms with onlyone degree of freedom joints, where overall mobility of

the mechanism is unity. Substituting F=1 and h=0 inKutzbach equation


0423

02)1(31

jL

or

jL

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Reference: Theory of machines S.S.RATTAN PP2155KHALID/SMBS/VITU/WINTER 2015165/01/2016


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Grashoffs Type2: s+l > p +q


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no complete rotatable joints

Grashoffs law neutral: s+l= p+q

linkages can be flattened



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Transmission Angle


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Min. transmission

angle

Max. transmission angle

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Transmission angle


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Crankrocker

doublerocker


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Mechanical advantage


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INVERSIONS OF MECHANISM

A mechanism is one in which one of the links of a kinematic

chain is fixed. Different mechanisms can be obtained by fixingdifferent links of the same kinematic chain. These are called asinversions of the mechanism.


FOUR BAR CHAIN


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(link 1) frame (link 2) crank

(link 3) coupler (link 4) rocker


INVERSIONS OF FOUR BAR CHAIN


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INVERSIONS OF FOUR BAR CHAIN

1. Crank-rocker mechanism

2. Drag link mechanism

3. Double rocker mechanism


CRANK ROCKER MECHANISM


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CRANKROCKER MECHANISM


DRAG LINK MECHANISM


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DRAG LINK MECHANISM


DOUBLE CRANK MECHANISM


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SLIDER CRANK CHAIN


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INVERSIONS OF SLIDER CRANK CHAIN


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(a) crank fixed (b) connecting rod fixed (c) slider fixed


INVERSIONS OF SLIDER CRANK CHAIN


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(a) crank fixed (b) connecting rod fixed (c) slider fixed


First Inversion fix link no.1


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2crank4 slider

Link 1 fixed

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IC Engine

Compressor

Second Inversion fix link no.2 (crank)


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Fixing link No2

Rotary Engine mechanism

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Whitworth quick return motion mechanism 2 Inversion


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Rotary engine 2 inversion of slider crank mechanism. (crank fixed)


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Third Inversion


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Fixing link No3Oscillating cylinder engine

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Crank and slotted quick return motion mechanism


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Fourth Inversion

Fixing link No4


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g

Hand Pump

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DOUBLE SLIDER CRANK CHAIN


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It is a kinematic chain consisting of twoturning pairs and two sliding pairs.


SCOTCH YOKE MECHANISM


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Turning pairs ? Sliding pairs ?


Elli ti l t l

Inversions of double slider crank mechanism


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Elliptical trammel

1sincos 2222

p

y

q

x

AC = p and BC = q, then,x = q.cos and y = p.sin.

Rearranging,


Oldhams Coupling


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FOUR BAR MECHANISM


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Straight line motion mechanisms


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Condition for perfect steering Locus of pt.C will be a straightline, to AE if,

is constant.Proof:

ACAB

..,

.

constACifABconstAE

constbutAD

AD

ACABAE

AE

AB

AC

AD

ABDAEC


Peaucellier mechanism


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Harts mechanism


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Scott Russells mechanism


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Roberts mechanism


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Intermittent motion mechanisms

Geneva wheel mechanism


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Application of Ratchet Pawl mechanism


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Other mechanisms


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Toggle mechanism

Considering the equilibriumcondition of slider 6,

For small angles of , F ismuch smaller than P.

tan2

2tan

PF

P

F


Pantograph


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Kinematics of Machinery Unit 1

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